Special Relativity | Part IB, 2001

A particle of mass MM is at rest at x=0x=0, in coordinates (t,x)(t, x). At time t=0t=0 it decays into two particles A\mathrm{A} and B\mathrm{B} of equal mass m<M/2m<M / 2. Assume that particle A moves in the negative xx direction.

(a) Using relativistic energy and momentum conservation compute the energy, momentum and velocity of both particles AA and BB

(b) After a proper time τ\tau, measured in its own rest frame, particle A decays. Show that the spacetime coordinates of this event are

t=M2mτx=MV2mτ,\begin{aligned} t &=\frac{M}{2 m} \tau \\ x &=-\frac{M V}{2 m} \tau, \end{aligned}

where V=c14(m/M)2V=c \sqrt{1-4(m / M)^{2}}.

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